ISSN: 1693-6930
TELKOMNIKA Vol. 13, No. 1, March 2015 : 155 – 163
156 system is the three-dimensional description of the color perception. Each color can be
represented by a dot in the color space.
2.1. Characteristics of Impulse Noise
In image processing, impulse noise, that is, salt-pepper noise, will cause black and white dots in the image, especially, in parts where are very dark or very bright. Generally
speaking, the pixel grayscale value in the image is a continuous gradation. The grayscale of the impulse noise dot is the superposition of the normal grayscale of this dot and the noise
grayscale.
When a pixel in the image is interfered by the impulse noise, its grayscale value will differ greatly from those of the adjacent pixels. When the noise grayscale is positive, it appears
in the image as an isolated bright dot. When the impulse noise grayscale is negative, it appears as an isolated dark dot. Impulse noise dot and the typical variation characteristics of the
neighborhood pixel grayscale of are shown in Figure 1 a and b:
a b Figure 1. Impulse noise model
2.2 Weighted Vector Direction Distance Filteringof the Image
The natural image is non-stationary. The premise of filtering operation is that the image can be divided into several smaller areas, and each area can be regarded as stationary. The
smaller image area is determined by the support window. Filter window is an important part of spatial filtering, which is related to the size of the window, directionality and partition, etc. All the
pixels
1 2
, , ,
N
W x x
x
in a window around the center pixel, is shown in Figure 2:
Figure 2. Pixels in the window In 1993, Trahanias put forward the Basic Vector Directional Filter BVDF, which is a
method based on the direction information in color vectors. In 1995, Karakos put forward the Directional-distance Filters DDF, which integrates the methods of Vector Median Filter VMF
and BVDF. They have a common drawback, that is, they all neglect that the pixels in the filter x1 x2 x3
x4 x5 x7 x8 x9
i or j i or j
TELKOMNIKA ISSN: 1693-6930
Color Image Enhancement Based on Ant Colony Optimization Algorithm Haibo Gao 157
window are also related to space distance. This crucial point will affect the result of image filtering. However, weighted vector direction distance filter can make up this drawback.
Weighted vector filter means that each pixel in the weighted vector filter has a corresponding weight value. The filter result is represented through the space distances between the pixels in
the filter window [5].
In weighted vector direction distance filter, each pixel in the same filter window has two corresponding weight value, which concerns two factors, one is vector direction, and the other is
vector distance. In the filter window, suppose there are k pixels
, ,
, ,
1 2
1 2
, ,
, ,
p q p q
p q p q
K K
Z Z
Z Z
, using
1 2
, ,
K
w w w
to represent the coefficient of the vector distance weight value, using
1, 2, ,
r
w r K
to represent the real number, whose range is [0,1], multiplying weighted vector distance with weighted angle distance, whose produce can be represented with
, p q
r
,
, p q
r
represents the weighted vector direction distance, as shown in the following:
1 1
1 1
1 1
1 ,
, ,
, ,
1 1
1 1
1
, 1, 2,
K K
y p q
p q p q
p q p q
r r
r r
r r
r r
r r
r r
r
w z
z w A z
z r
K
1
In the filter window, using represent vector distance and vector angle, that is, the
output. If each pixel
,
1, 2,
p q r
z r
K
in
, p q
is sequenced in an ascending order according to the vector distance
, i j
r
in 1, and gain the result after sequencing
, ,
, ,
1 2
1 2
, ,
, ,
p q p q
p q p q
K K
z z
z z
, then
, ,
1 p q
p q
Y z
represents that the filter keeps calculating till gaining the correct result. Therefore, such filtering is called weighted vector direction distance
filtering [6].
3. Principle and Application of Ant Colony Algorithm 3.1. Basic principle and idea of ant colony algorithm
1 Basic idea Ant colony algorithm is the imitation of ant foraging behavior in the nature. During the
ant foraging process in the nature, although there are many barriers between ant nest and food source, ants have always been able to bypass obstacles and find the shortest path between the
nest and source to acquire food. When the exterior environment is changed, the ants can quickly adapt to such change to find new optimal path. The main reason lies in the mechanism
of communication among the ants. This mechanism is the pheromone which is an important channel for ants to communicate with each other, which at the same time also makes ants
always tend to select the path with higher pheromone density in the process of searching for food.
2 Ant’s path search Such a positive feedback mechanism will also occur when ants meet obstacles. As
shown in the following Figure 1, assume that A is the ant nest and D the food source, when the ant reaches B from A, the ant will reach C by selecting randomly to pass E or F, and leave
pheromones along the way. At first, with the same probability, all ants will select E or F to bypass the obstacle, in this way, the pheromone density on path BE and BF are same in a short
period of time. But with the passage of time and the pheromone volatility, pheromone density on path BE is relatively low than BF due to the path BE is longer than path BF. In selecting the
path, subsequent ants will tend to select path BF, and in this way, the pheromone density on path BF will further increase, while, the pheromone density on path BE will sharply decrease
due to the ant number selecting path BE decreases, and then the ant number selecting such path will sharply reduce, thus a new positive feedback mechanism will be formed and finally all
ants tend to select one shortest path to bypass obstacles in order to reach the food source [7].
ISSN: 1693-6930
TELKOMNIKA Vol. 13, No. 1, March 2015 : 155 – 163
158
Figure 3. Ant colony foraging sketch map We can see that during the foraging process, all ants coordinate with each other.
Although, the ant number in the entire ant colony is numerous, the entire ant colony reflects the self-organizing characteristic, and following principles should be met to complete such
characteristic: 1 Search range
The individual ant is very tiny and its perceptive range is very limited. Usually, the range that one ant is able to observe is a checkered world. This range is the 33 check with 8
directions and its advancing distance of only 1. The ant step search is only within such a small range.
2 Ant search environment The environment where artificial ants are in is a virtual world in which the ant will also
encounter obstacle when searching, and this obstacle is also a kind of visual existing forms. In order to make the ants have large search range possibly, we assume a volatile mechanism for
the pheromone released by ants during the moving process to make the virtual environment more close to the ant’s environment in the nature possibly.
3 Search rule Search whether there is any food in the range that can be perceived by each ant, and
get over if there is food, otherwise, check whether there is any pheromone. Select the point with the most pheromones within the range that can be perceived and move to this point with larger
probability, that is to say, each ant will make mistakes in small probability and does not always move towards the point with the most pheromones. The rule that ants finding the nest is similar
to the above, but it only responds to nest pheromones.
4 Move rule Each ant moves towards the direction with the most pheromones in larger probability,
but when there is no pheromone to guide, the ant will move on according to the original move direction and there may be small random disturbance along the move direction. In order to avoid
circling around, the ant can remember and avoid the position where it has gone when moving. 5 Obstacle avoidance rule
If there are obstacles blocking the direction where the ant is to move, the ant will randomly choose another direction, and will move according to the rules of foraging behavior
under the guidance of the pheromone. 6 Disseminating pheromone rule
The pheromone disseminated by each ant at the time when it finds the food or the nest is the most, which becomes fewer and fewer as the moving distance increases.
According to these few simple rules, there is no direct relationship among ants, but each ant interacts with the environment and is associated together by the pheromone bond[8,9].
3.2. Basic ant colony algorithm applied to TSP
